Chemo-dynamical reconstruction of Milky Way globular cluster progenitors: age--metallicity relations and the universality of multiple stellar populations

Abstract

Globular clusters encode the hierarchical assembly history of the Milky Way and the physics of multiple stellar populations. Using homogeneous stellar parameters for 69 Galactic globular clusters derived while modelling multiple populations, we reconstruct progenitor-specific age--metallicity relations (AMRs) and test whether helium-related multiple-population (MP) properties depend on progenitor origin once cluster mass and metallicity are controlled for. Ages, helium spreads ($δY$), mean helium abundances ($\bar{Y}$), and first-population fractions ($f_{\rm P1}$) are drawn from hierarchical Bayesian CMD modelling. Progenitor families are identified via chemo-dynamical clustering, AMRs reconstructed within a hierarchical Bayesian framework, and MP indicators tested for environmental dependence. Enrichment timescales are consistent with $τ\lesssim 2$\,Gyr, though individual progenitors prefer shorter values when fitted independently. The primary distinction is the extent of chemical evolution: most systems reach $Δ[\mathrm{Fe/H}] \sim 1.1$--$1.3$\,dex while Sagittarius achieves ${\sim}1.6$\,dex and higher terminal metallicities. Gaia--Sausage--Enceladus and low-energy/Kraken are the dominant accretion events. Neither $δY$ nor $\bar{Y}$ depends on progenitor origin; the mass--MP scaling is indistinguishable across in-situ and accreted systems. Sequoia clusters alone show higher $f_{\rm P1}$ at fixed mass and metallicity. AMRs carry fossil signatures of progenitor chemical evolution and mass hierarchy. Helium enrichment amplitude is regulated by cluster mass and blind to environment, pointing to universal cluster-scale formation physics, with the sole exception of a residual dependence in $f_{\rm P1}$, suggesting the enriched-star fraction retains a secondary environmental imprint.

Figures (7)

• Figure 1: Integrals-of-motion projections for the MW GC sample coloured by our final six-family probabilistic classification. Left:$E$--$L_z$ plane; right:$E$--$L_\perp$. Colours/markers denote the assigned family (see legend). We define the classification confidence using the maximum posterior probability $p_{\max}$ and the probability margin $\Delta p = p_{\max}-p_{\rm 2nd}$ between the two most probable classes. Objects are considered secure when $p_{\max}\ge0.80$ and $\Delta p\ge0.20$, likely when $p_{\max}\ge0.60$ and $\Delta p\ge0.10$, and ambiguous otherwise. For clarity, cluster names are shown only for the objects with likely or ambiguous classifications (see Table \ref{['tab:cluster_summary']}).
• Figure 2: Box-and-whisker plots showing the distributions of $[\mathrm{Fe/H}]$ (top) and $[\alpha/\mathrm{Fe}]$ (bottom) for GCs associated with each progenitor family.
• Figure 3: Age--metallicity relations for the final merged progenitor groups. Each panel shows individual GCs (points) with asymmetric age and metallicity uncertainties, grey shaded kernel-density contours highlighting the main population distribution, and the ODR linear fit (dashed line) accounting for errors in both variables. The linear fits provide a visual diagnostic of the overall AMR trend within each progenitor; however, they should not be interpreted as physical enrichment rates, as the inferred slopes depend sensitively on the sampled age range.
• Figure 4: Hierarchical Bayesian AMRs for accreted MW progenitors traced by GCs. Top left panel: absolute lookback age versus $[\mathrm{Fe/H}]$, with observational uncertainties shown as error bars. Solid lines indicate the posterior median AMR for each progenitor, while shaded regions represent the 68% (dark) and 90% (light) credible intervals derived from posterior samples. Top right panel: the same relations expressed in relative time since enrichment onset, $\Delta t = L_0 - t$, highlighting the inferred enrichment duration prior to truncation. Lower panels: posterior credible intervals for key chemical evolution parameters of the accreted progenitors. For each system, the median value is shown as a filled circle, thick horizontal bars denote the 68% credible interval, and thin bars indicate the 90% credible interval. Displayed parameters include the truncation lookback time $L_{\rm stop}$, enrichment timescale $\tau$, total metallicity increase $\Delta[\mathrm{Fe/H}]$, and terminal metallicity $[\mathrm{Fe/H}]_{\rm stop}$. The results illustrate broadly similar enrichment timescales across progenitors, with Sagittarius distinguished by larger enrichment amplitude and higher terminal metallicity.
• Figure 5: Progenitor stellar masses inferred from the AMR subsample compared to dynamical constraints. Grey shaded boxes indicate the allowed progenitor stellar-mass ranges inferred from GC orbital information in E-MOSAICS by pfeffer20. Black points show the chemistry-only $M_\star$ posteriors obtained by inverting the dwarf MZR using the AMR-inferred $[\mathrm{Fe/H}]_{\rm stop}$ (error bars are the 16th--84th percentiles from MC propagation). Red points show the corresponding importance-weighted posteriors after applying the pfeffer20 mass constraints as a prior in $\log M_\star$.